beats and cents

[Richard Moody]

Better late than never... had modem problems.......

Paul Chick wrote....

+AHw-Being an aural tuner I can
+AHw- relate to beat rates easier than cents deviations.

Same here.   The cents deal is an exercise in mathematics
that is more of a hobby than a necessary chunk of knowledge
needed to know how to tune by ear.
Our musical scale has a mathematical basis  because it obeys
the simpler laws of physics relating to frequency.

One of these laws is that two frequencies nearly the same
will produce a phenomon known as a beat, or a beat frequency
that is exactly the numerical diffrerence between the two
frequencies.   If you are setting A440 from the fork and you
hear a beat of one beat per second (bps) you are either at
441 or 439.The arithmetic here is self evident.
If you are setting the octave down from A440 or A4--A3, and
you hear a beat of one cycle per second you are either at
220.5 or 219.5.   Here it is not as simple until you realize
the beat is caused by difference between the fundamental
frequency of A4 and the frequency of the second partial of
A3.    Here the harmonic series of musical tones comes into
play and how the partial series of a vibrating piano wire is
close to that.  So to hear a beat of one cycle per second
between A4 and A3 you are hearing the 440 already tuned and
the second partial (also called coincident partial) of the
A3 you are tuning which would be either 441 or 439. Now it
is easy to see where a beat of 1 per second comes from.
Since this is the second partial, the fundamental freq would
be half of that ie  220.5 or 219.5

    This is just the beginning, there are books where
everything is well explained. The classic is Wm Braid White,
+AF8-Piano Tuning and Allied Arts+AF8-.   A more modern book is
Piano Servicing  by Art Reblitz.   A  comprehensive
explaination for the physics and math basis is +AF8-The Piano
its Acoustics+AF8- by McFerrin.     All three of these books can
be gotten from the supply houses, and many municipal
libraries.   It is important to understand the harmonic
series and how coincident partials occur in the various
intervals as this is the source of beats used in tuning.

    For understanding cents there was an article in the
Journal  back in 2000 written by a piano tuner for piano
tuners,   +ADs- )  (I heard he was contemplating an article
titled something like +ACI-Intrigue of the Intervals+ACI- but
between the first note and the lost chord could easily go 10
chapters).   But one only needs know how to use the cents
formula rather than understanding that cents are actually
logs of the base of two (multiplied by 1200) but have to be
arrived at by converting  logs of base 10.   And you only
need to know this formula if you working with spread sheets
or want to figure out the cents value of various
als.       ---ric


----- Original Message -----
From: Paul Chick (EarthLink) +ADw-tune4+AEA-earthlink.net+AD4-
To: +ADw-pianotech+AEA-ptg.org+AD4-
Sent: Wednesday, June 05, 2002 8:10 AM
Subject: Re: trichords unisons


+AHw- Richard
.  Being an aural tuner I can
+AHw- relate to beat rates easier than cents deviations.  The
math/science of
+AHw- tuning is not my strong suit.  Do you know of a book that
would explain
+AHw- this?  My curiousity is getting to me.
+AHw-
+AHw- Paul Chick+AHw- ----- Original Message -----
+AHw- From: +ACI-Richard Moody+ACI- +ADw-remoody+AEA-midstatesd.net+AD4-
+AHw- To: +ACI-Pianotech+ACI- +ADw-pianotech+AEA-ptg.org+AD4-
+AHw- Sent: Tuesday, June 04, 2002 11:51 PM
+AHw- Subject: Re: trichords unisons
+AHw-
+AHw-
+AHw- +AD4-
+AHw- +AD4- +AD4- The difference between 440 and 439 is almost 4 cents.
+AHw- +AD4- From 880 to 879 nearly 2 cents.   From 1760 to 1759
almost 1
+AHw- +AD4- cent.